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​in the given figure, O is the centre of the circle if angle BOC =120,the find the value of x ?

Dear Student,

Please find below the solution to the asked query :

We have :∠BOC = 120°now, ∠AOC + ∠BOC = 180°   Linear pair⇒∠AOC + 120° = 180°⇒∠AOC = 180° - 120°⇒∠AOC = 60°We know that angle subtended by an arc at the centre is double the angle subtended by the same arc at any point on the circle.Now, ∠AOC = 2∠ADC⇒60° = 2x⇒x = 30°
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angle AOC = 180-120=60 (linear pair)
angle ADC = x = 60/2 = 30 degree (angle subtended on the centre is the double of the angle subtended on the remaining part of the circle i.e. angle AOC = 2(angle ADC)

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